EUM is also called the Population Utility (PU) in [1]}.
It learns a classifier by maximizing the corresponding empirical measures based on the training data
and then predicts an unseen instance by using the learned classifier.
Several works have applied the traditional algorithms, such as SVM and logistic regression, to the
non-decomposable performance measure maximization by replacing the error rate with a specially designed
surrogate loss function [2]}, [3]}, [4]}, [5]}.
Recently, studies are focused on the plug-in approach, which learns a class probability function first
based on a training example and then makes a decision of the threshold according to another data
set [6]}, [7]}, [8]}.
[9]} provided a general methodology to show the statistical consistency of the plug-in
approach for any performance measure that can be expressed as a continuous function of the true positive
and true negative rates as well as the class proportion, such as \(F_\beta \)  and the Geometric Mean (GM) of
TPR and TNR. Cost-sensitive classification is also used in this approach, which learns a classifier by
minimizing a weighted False Positive Rate (FPR) and False Negative Rate (FNR).
[6]} proved the consistency of the empirically cost-sensitive learning algorithm concerning
the Arithmetic Mean (AM) of the TPR and TNR metrics, in which the cost parameter is determined from the
empirical class ratio.
A cost-sensitive Support Vector Machine (SVM) with a tuning threshold was proposed in [11]}
for the metric \(F_\beta \) , where the cost parameter is searched with a grid-based method.
[12]} presented the Cone-based Optimal Next Evaluation (CONE) algorithm that iteratively
selects the classification costs that lead to a near-optimal \(F_\beta \) -measure.
As discussed in Section , many non-decomposable performance measures except AM aim at minimizing
a polynomial combination of FPR and FNR rather than a linear combination of them.
The cost-sensitive learning approach seems not an appropriate method for these metrics.
